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Explain the origin of spectral lines of hydrogen using Bohr's theory. |
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Answer» Solution :According to Bohr.s theory of hydrogen atom we know that a radiation photon of energy (E = h V) is emitted when transition of an electron TAKES place from a higher energy state `E_(i)` corresponding to a shell with principal quantum number `n_(i)` to a lower energy state Escorresponding to a shell with principal quantum number `n_(f)` (where `n_(f) lt n_(i) or n_(i)gt n_(f) `). `therefore "" hv = E_(i) -E_(f)` But as per Bohr.s theory, the energy of an electron in its state corresponding to n level is `E_(n) =- (me^(4))/(8 in_(0)^(2) n^(2) h^(2))` `therefore "" h v = E_(i) = E_(f) = - (me^(4))/(8 in_(0)^(2)n_(i)^(2) h^(2)) + (m e^(4))/(8 in_(0)^(2) h^(2)) [(1)/(n_(f)^(2)) - (1)/(n_(i)^(2))]` `rArr ` Frequencyof spectral line `v = (me^(4))/(8 in_(0)^(2) h^(3))[(1)/(n_(f)^(2))- (1)/(n_(i)^(2))]` , where`n_(i)` and `n_(f)`are bothintergers and `n_(i) gt n_(f)`andwavelenghtof spectral line is giveby . `(1)/(lambda) = bar(v) = (v)/(c)= R [ (1)/((2)^(2)) - (1)/(n^(2))] `, where n = 3,4,5,6. whichis the empirical relation for spectral lines of Balmer seires . Similarly , ifwe put`n_(f) = 1`and `n_(i) = n = 2 , 3,4,5,............,we get empirical relation for Lyman series . On SUBSTITUTING`n_(f) = 3,4,5 ` and`n_(i) gt n_(f)` , we getrelationfor Paschen series,Bracket series and Pfundseries of hydrogen atom respectively . |
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